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MatLAB
Write a MATLAB program to solve the following BVP
. Perform two iterations to solve the following one dimensional heat equation
using FTCS and Crank−Nicolson scheme, with ∆x =
1
4
.
∂u
∂t = 4
∂
2u
∂x2
, 0 < x < 1, t > 0.
u(0, t) = u(1, t) = 0, t ≥ 0 and u(x, 0) = x(1 − x), 0 < x < 1.
. Perform two iterations to solve the following one dimensional heat equation
using FTCS and Crank−Nicolson scheme, with ∆x =
1
4
.
∂u
∂t = 4
∂
2u
∂x2
, 0 < x < 1, t > 0.
u(0, t) = u(1, t) = 0, t ≥ 0 and u(x, 0) = x(1 − x), 0 < x < 1.
MatLAB
. Write a MATLAB program to solve the following BVPs
. Solve the following BVP
∇2u = 0, 0 ≤ r ≤ 1, 0 ≤ θ ≤ π
with boundary conditions
u(1, θ) = 4
π
(πθ − θ
2
), u(r, 0) = u(r, π) = 0, u(0, θ) < ∞.
. Solve the following BVP
∇2u = 0, 0 ≤ r ≤ 1, 0 ≤ θ ≤ π
with boundary conditions
u(1, θ) = 4
π
(πθ − θ
2
), u(r, 0) = u(r, π) = 0, u(0, θ) < ∞.
MatLAB
Write a MATLAB program to solve the following BVP
Solve the following boundary value problem using finite difference method,
with ∆x = ∆y =
1
3
∂
2u
∂x2
+
∂
2u
∂y2
= 0, 0 < x < 1, 0 < y < 1
u(x, 0) = u(0, y) = 0, u(x, 1) = x, u(1, y) = y, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
Solve the following boundary value problem using finite difference method,
with ∆x = ∆y =
1
3
∂
2u
∂x2
+
∂
2u
∂y2
= 0, 0 < x < 1, 0 < y < 1
u(x, 0) = u(0, y) = 0, u(x, 1) = x, u(1, y) = y, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
MatLAB
Write a MATLAB program to solve the following two-point boundary
value problems and then compare numerical solutions graphically
(b) d
2
θ
dt2
= − sin(θ(t)), 0 < t < 2π, θ(0) = 0.7, θ(2π) = 0.7
value problems and then compare numerical solutions graphically
(b) d
2
θ
dt2
= − sin(θ(t)), 0 < t < 2π, θ(0) = 0.7, θ(2π) = 0.7
MatLAB
Write a MATLAB program to solve the following two-point boundary
value problems and then compare numerical solutions graphically.
(a) d
2
θ
dt2
= −θ(t), 0 < t < 2π, θ(0) = 0.7, θ(2π) = 0.7
value problems and then compare numerical solutions graphically.
(a) d
2
θ
dt2
= −θ(t), 0 < t < 2π, θ(0) = 0.7, θ(2π) = 0.7
MatLAB
. Write a MATLAB program to the method of undetermined coefficients
for approximating d
ku(xr)
dxk
, k = 1, 2, 3 and xr is a reference point.
for approximating d
ku(xr)
dxk
, k = 1, 2, 3 and xr is a reference point.
MatLAB
Write a MATLAB program to solve the following BVPs
. Solve the following PDEs
∂
2u
∂t2
=
∂
2u
∂x2
, 0 < x < 1, t > 0.
u(x, 0) = 0,
∂u
∂t
(x,0)
= sin3
(πx), 0 ≤ x ≤ 1
u(0, t) = u(1, t) = 0, t ≥ 0.
. Solve the following PDEs
∂
2u
∂t2
=
∂
2u
∂x2
, 0 < x < 1, t > 0.
u(x, 0) = 0,
∂u
∂t
(x,0)
= sin3
(πx), 0 ≤ x ≤ 1
u(0, t) = u(1, t) = 0, t ≥ 0.
MatLAB
Write a MATLAB program to solve the following BVPs
Perform two iterations to solve the following one dimensional heat equation
using FTCS and Crank−Nicolson scheme, with ∆x =
1
4
.
∂u
∂t = 4
∂
2u
∂x2
, 0 < x < 1, t > 0.
u(0, t) = u(1, t) = 0, t ≥ 0 and u(x, 0) = x(1 − x), 0 < x < 1.
Perform two iterations to solve the following one dimensional heat equation
using FTCS and Crank−Nicolson scheme, with ∆x =
1
4
.
∂u
∂t = 4
∂
2u
∂x2
, 0 < x < 1, t > 0.
u(0, t) = u(1, t) = 0, t ≥ 0 and u(x, 0) = x(1 − x), 0 < x < 1.
MatLAB
Write a MATLAB program to solve the following BVPs
Solve the following BVP
∇2u = 0, 0 ≤ r ≤ 1, 0 ≤ θ ≤ π
with boundary conditions
u(1, θ) = 4
π
(πθ − θ
2
), u(r, 0) = u(r, π) = 0, u(0, θ) < ∞.
Solve the following BVP
∇2u = 0, 0 ≤ r ≤ 1, 0 ≤ θ ≤ π
with boundary conditions
u(1, θ) = 4
π
(πθ − θ
2
), u(r, 0) = u(r, π) = 0, u(0, θ) < ∞.
MatLAB
let T[2 3 pi: 8 pi/2 1] calculate the square root,natural logarithm e^s and facorial of each element of the matrix S.
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